JEE Main 2024 Mathematics question
The number of integers, between 100 and 1000 having the sum of their digits equals to 14, is .
Answer: 70
Solution
Let the number be abc with a ≥ 1 and a + b + c = 14. All three digits different: the digit sets without 0 are {6,5,3}, {7,6,1}, {7,5,2}, {7,4,3}, {8,5,1}, {8,4,2}, {9,4,1}, {9,3,2}, giving 8 × 3! = 48 numbers; the sets with 0 are {8,6,0} and {9,5,0}, giving 2 ×
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